Problem: Multiply the following complex numbers: $({-5-2i}) \cdot ({-1-i})$
Solution: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-5-2i}) \cdot ({-1-i}) = $ $ ({-5} \cdot {-1}) + ({-5} \cdot {-1}i) + ({-2}i \cdot {-1}) + ({-2}i \cdot {-1}i) $ Then simplify the terms: $ (5) + (5i) + (2i) + (2 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 5 + (5 + 2)i + 2i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 5 + (5 + 2)i - 2 $ The result is simplified: $ (5 - 2) + (7i) = 3+7i $